Polishing stainless is a mother fu--er of a time. You really have to breakdown the metal in steps. Start with a corse pad(180) then step down to a fine pad (250)then put some black rubbing compound on the fin pad. Then take it to the buffer! Start with a course cotton wheel with black compound. After that buff with loose cotton wheel using green, then finishing with white compound. Then I will usually hand buff with Flitz. So it is a long and dirty process and takes some practice but the end result is stunning! We have a foundry in my town that will cast stainless, so let me know in the future if you want more info.
Wow thats a crazy process, Have you ever tried the plastic bristle wheels that 3M makes? I use the coarse ones on steel and they are incredibly smooth and remove material very well. Might be worth playing with.